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iik 









MANUAL 


DW 

£\\ 



FOR THE USE OF 


THE PRACTICAL MILTER. 


BY 


T. F. VAN WAGENEN, E.M. 


M 


Jfc . /Oili 



New York : 



1). VAN NOSTRAND, PUBLISHER, 

23 MURRAY & 27 WARREN STS. 

1880. 





TN -VM 
•V z.% 


Copyrighted by 
D. VAN NOSTRAND. 
1880. 









PREFACE. 


The following pages are written solely for 
the use of the practical and working miner, 
who, while rarely deficient in common sense, 
is generally unacquainted with the principles of 
physics and more or less rusty in arithmetical 
methods. In the daily discharge of his business 
he is continually confronted with engineering 
problems of more or less complexity, and com¬ 
pelled to depend for their solution—trained en¬ 
gineering advice being unobtainable or too ex¬ 
pensive—upon his own limited experience or 
upon that of his co-laborers. 

Under these circumstances, errors in con¬ 
struction and operation are frequently repeated. 
The author ventures the hope that the study and 
use of the following pages will, to some extent 
at least, obviate the necessity for costly experi¬ 
menting, now so common. 

3 



4 


PREFACE. 


The Manual does not claim to cover the whole 
subject, nor to answer all‘questions in hydraulic 
engineering. Nor will it take the place of an 
experienced and competent engineer in impor¬ 
tant enterprises. On the contrary, no miner 
who is not himself an expert, and who can af¬ 
ford it, should be without such advice and assis¬ 
tance as can be afforded by a well-educated 
and practised hydraulic engineer. 

Theo. F. Van Wagenen. 




CONTENTS. 


PAGE. 

Introductory Remarks, . . . .7 

CHAPTER I. 

General Physical Conditions, . c .11 

CHAPTER II. 

General Methods of Placer-Mining, . . 19 

CHAPTER III. 

Directions for the Miner, . . . .25 

CHAPTER IV. 

The Properties of Water, . . . .43 

CHAPTER V. 

Construction of Water-Ways, . . .51 

CHAPTER VI. 

Flow of Water in Flumes and Ditches, . . 58 

CHAPTER VII. 

Iron Piping, . . . . . .64 

CHAPTER VIII. 

Nozzles and Discharge, . . . .79 

CHAPTER IX. 

The Sluice, . . . . . .82 






INTRODUCTORY REMARKS. 


Hydraulic mining is the art of separat¬ 
ing gold from gravel, sand, and clay cement, 
through the medium of moving water and the 
force of gravity. 

The process is one lying wholly within the do¬ 
main of the science of mechanics—a branch of 
human knowledge now so well understood that 
results may be predicated with extreme accura¬ 
cy, if correct premises are obtained. 

Hence, hydraulic mining presents fewer risks 
and more certainties than any other department 
of mining, other things being equal. It is sim¬ 
ply a question of moving gravel or soil from one 
place to another. Given, therefore, in addition 
to an abundance of water to move and wash the 
gravel, ample space to deposit it again after it 
has been washed, and the problem of obtaining 
a profit is reduced to a minimum. 

7 



8 


INTROD UCTOR Y REMARKS. 


Gold occurs in gravel deposits in a metallic 
condition. The chemical and mechanical ope¬ 
rations required to separate it from the vein 
substances with which it was originally asso¬ 
ciated have all been performed by nature. That 
wonderful agency has also supplemented her 
work by again collecting the particles of metal 
within certain limits. In other words, degrada¬ 
tion and erosion of quartz-veins has been fol¬ 
lowed by the partial concentration of the mate¬ 
rial so broken up; and while this operation has 
not resulted in an enrichment of the gold-bear¬ 
ing material (on the contrary, it is much poorer, 
bulk for bulk), the metal is placed in association 
with substances from which it may be separated 
with ex're me ease and very small cost. 

As an example, the gold-bearing veins of the 
western United States have an average value of 
about ten dollars per ton of quartz extracted, 
which ten dollars can be mined, transported to 
mill, crushed, amalgamated, refined, and sold at 
a gross cost of about eight dollars per ton, or 
eighty per cent. The same gold vein, after pass¬ 
ing through the laboratory of nature, will consist 


INTRODUCTORY REMARKS. 


9 


of a gravel-bed or deposit worth about twenty 
cents per ton, which twenty cents may be se¬ 
cured and marketed at a cost not over five cents, 
or twenty-five per cent. Other things being 
equal, therefore, hydraulic mining presents three 
times the chance for profit that is found in 
gold quartz-mining, and one-third the risk, with 
the additional advantage that the extent and 
richness of the gravel-bed may be completely 
studied and ascertained before working it, and 
at a slight cost ; while vein-mining is from 
first to last more or less of an experiment and 
a chance. 

The records of mining show that over seventy- 
five per cent, of all the gold mined within his¬ 
toric times has been derived from the working 
of gravel-beds. It is also a matter of fact that 
the area of auriferous gravel deposits is vastly 
greater than that.of quartz-veins. This is es¬ 
pecially the case on the Pacific coast of both 
North and South America. The immense chain 
of mountains extending from Alaska to Pata¬ 
gonia bears evidence of having been at once one 
of the loftiest and oldest of the great upheavals 




io 


INTRODUCTORY REMARKS. 


of geological time. From one extremitv to the 
other it is ribbed with metallic veins, which 
through the ages have been worn down and 
away, and their debris deposited by rivers and 
lakes and glaciers in all the various ways in 
which nature works. And these great deposits, 
consisting of old channel-beds, forsaken bars, 
grass and forest covered moraines, and sterile 
terraces, contain, beyond a doubt, more millions 
than have yet been mined. The great Blue Lead 
of California, which has been traced for seven 
hundred miles along the western flank of the Si¬ 
erras ; the channels and bars of Montana, which 
represent the pathway of the Missouri of old ; 
the great morainal deposits of Western Colorado, 
and the arid and dry terraces and ravines of 
Arizona—all these are nature’s gold-filled vaults, 
inviting the enterprise, the energy, and the in¬ 
genuity of the white man, and promising, not 
the irregular and doubtful returns which charac¬ 
terize precious-metal mining of the present day, 
but steady and continuous results, based on an 
industry as legitimate and safe as agriculture or 
general trade. 




CHAPTER I. 


GENERAL PHYSICAL CONDITIONS . 

GRAVEL. 

Gravel deposits containing gold are gene¬ 
rally considered to be the disintegrated remains 
of mountains which were originally seamed with 
auriferous quartz-veins, or of strata of rock in 
which the metal was dissemiuated, or both. 
The material forming these deposits consists of 
gravel, rounded boulders, sand, and clay, gene¬ 
rally being in conformable layers or strata, but 
at times disposed without regularity. These de¬ 
posits are be\ond doubt the result of mechanical 
precipitation. The occurrence of gold dissemi¬ 
nated through the gravel is generally ascribed to 
the same cause, though some are inclined to be¬ 
lieve that chemical action has supervened in the 
case of the metal. The point is one of more 
scientific than practical interest, though the lat- 


12 


HYDRA ULIC MINING. 


ter theory will perhaps explain why placer gold 
is purer than vein gold. 

Gravel deposits may be subdivided as follows: 

(a) Ancient river-channels. 

(b) Kecent “ “ 

( c ) Bars. 

(cl) Moraines. 

(e) Terraces. 

(/) Lake-bottoms (ancient and recent). 

In general it may be stated that gold will be 
found in greater quantities and in coarser frag¬ 
ments in deposits which are— 

1. Nearest to the original deposits. 

2. Have been deposited on the steepest grades. 

3. Contain the most gravel and boulders. 

4. Contain the most iron. 

There are many cases in America, however, 
where the gold is found almost exclusively in the 
clay or cement layers, but this does not appear 
to be the rule. 

Where gravel deposits are made up of several 
layers of differently-sized material, often some of 
these layers are wholly barren, or at least un¬ 
profitable. In general the metal is found in 


HYDRAULIC MINING. 


J 3 


greater quantities in the lower layers of the gra¬ 
vel, near and on the bed-rock. 

Frequently in exploring and testing gravel de¬ 
posits it is necessary or convenient to find the 
weight of the mass ; this operation will be facili¬ 
tated by the following table : 


One cubic ft. of dry, loose loam weighs.... 72 to 80 

“ .... 90 to 100 

“ _OGto 68 

“ .... 85 to 95 

“ ....165 

“ .... 94 

“ ....170 

“ .... 96 

“ ... 100 to 117 

“ .... 82 to 90 

“ “ ordinary gravel, free from 

cement, and containing no heavy boul¬ 
ders (dry), weighs. 90 to 100 

The same (wet) “ .80 to 90 

One cubic ft. filled with boulders not over 

six inches in diameter (dry) weighs. 95 to 105 

The same (wet) weighs. 85 to 95 


“ packed “ 
wet, loose “ 
“ packed “ 
solid quartz 
broken “ 
solid limestone 
broken ‘ ‘ 
fine sand, dry, 
“ wet, 


lbs. 


ii 
i i 


ii 

ii 

ii 

a 


ii 

ii 


ii 

ii 


Auriferous gravel deposits are formed on all 
kinds of bed-rock, such as granites, limestones, 
slates, and quartzites, and even sandstones. The 
nature of the bed-rock rarely, if ever, affects the 












M 


HYDRAULIC MINING. 


quality of tlic deposit, though, as will be seen 
hereafter, it may affect its economic value. 

GOLD. 

The precious metal is of a fine yellow color 
when chemically pure, and weighs about nine¬ 
teen times as much as an equal bulk or volume 
of water. Hence 


One cubic inch of gold weighs.68 lbs. 

One cubic foot “ “ .1175. “ 


Its value per standard Troy ounce is $27 67, 
and per pound (Troy) $332 04. 

In nature gold never occurs pure, but is inva¬ 
riably accompanied with some silver, and often 
with other metals. In this condition it presents 
a whitish or reddish yellow color, according as 
the bulk of the accompanying metal is silver or 
copper. 

The metal is exceedingly tenacious, malleable, 
and melts at a temperature of 2,01G deg. Tab. 

In practice its comparative purity is expressed 
bv the term fineness,” and this is estimated on 
the basis of 1,000 as a unit of measurement. 




II ) DR A ULIC MINING. 


T 5 


Thus, a mass or nugget of gold containing 78 
per cent, of gold, 18 per cent, of silver, and 4 
per cent, of other substances will be said to be 
.780 (seven hundred and eighty thousandths) 
fine. 

In the gravel deposits gold occurs as nuggets 
(masses of irregular shape and size) ; shot-gold 
(rounded pellets like very small bird-shot) ; 
leaf-gold (thin sheets sometimes one-tenth of an 
inch square) ; coarse flat gold (same size as the 
latter, but thicker) ; and dust , which is often so 
fine as to be inappreciable to the naked eye. 
Occasionally wire-gold is found, but that is rare. 
The physical qualities of this metal are such 
that, while it will remain almost wholly intact 
under the action of chemical reagents, it is 
easily affected by abrasion, and, if carried for 
considerable distances together with gravel and 
ice, is ground rapidly to the finest powder. 

It does not always follow that a gravel deposit 
containing even a goodly quantity of gold per 
yard can be worked with profit. The particles 
of metal, to be capable of being saved by cheap 
mechanical means, must possess a combination 


16 


HYDRAULIC MINING. 


of weight and shape which will permit the ac¬ 
tion of gravity to a maximum degree. In other 
words, if the bulk of the gold in a deposit is 
either in the condition of a very fine dust or 
very flat, thin scales, it will float away and resist 
the most careful endeavors to precipitate it. 


WATER. 

i 

At ordinary temperatures water is a clear, 

colorless liquid, weighing about 62^- lbs. per 

cubic foot. At 32 deg. Fall, it becomes a solid, 

and in the act of solidification expands one- 

twelfth of its volume. At 212 deg. (sea-level) 

• 

it boils, and passes off as vapor. Water is 
slightly compressible at a pressure of 4,500 lbs. 
per square inch, but on removal of the force re¬ 
turns instantly and completely to its former vol¬ 
ume. When expanding under the influence of 
heat or cold it is capable, as is well known, of 
exerting enormous force. 

The following table of equalities will be found 
at times useful: 


HYDRAULIC MINING. 


I/ 


1 cubic inch of water weighs.08G lbs. 

1 “ foot “ “ 62.5 

1 “ yard “ “ 1687.5 “ 

1 “ foot of ice “ 57.3 “ 

1 U. S. gallon “ . 8.32 “ 


The standard measure for water in hydraulic 
mining is the miner’s inch. 

The quantity of water which will escape from 
a reservoir through an aperture in its side 1 inch 
square, whose centre is G inches below the con¬ 
stant level of the water, is termed a miner’s 
inch. This measure is necessarily a rough one, 
and has doubtless been often erroneously ap¬ 
plied. The aperture should have no tube or 
conduit leading from it, and its section through¬ 
out should be uniform and possess practically no 
length. These conditions are not, however, at¬ 
tained in common practice. The most common 
illustration of the miner’s inch is a hole 1 inch 
square through an inch board. I 11 this case the 
length of the aperture is clearly equal to its dia¬ 
meter. Where the aperture discharges a large 
number of inches at once its diameter is of 
course much larger, and the proportion of its 
length to its diameter is much less. 








i8 


HYDRAULIC MINING . 


In round numbers the miner’s inch has the 
following values : 


Cubic feet. 

Discharge per second. .0271 = 
“ min... 1.6 = 


Pounds. U. S. gal. 
1.69 = 12.6 

100. = 756. 


“ hour.. 95. = 5937. = 45360. 

“ day (12h.) 1140. = 71250. = 544320. 

“ day (24h.) 2280. = 142500. = 1088640. 

The miner’s inch as a standard of water mea¬ 
surement is very defective. In the early days of 
placer-mining, when the water was owned by 
one set of people, who sold it in small quanti¬ 
ties to another set (the miners), tins standard 
was a necessity. At present it would be better 
if the cubic foot could be used as a measure, but 
the change is one impossible to be made. 


CHAPTER II. 


GENERAL METHODS OF PLACER-MINING. 

The general theory of hydraulic mining com¬ 
prehends—first, breaking down the gravel ; sec¬ 
ond, passing it through sluice-boxes while held 
in suspension by water; and, third, cleaning up 
the gold caught in the boxes. 

The pan, rocker, long tom, sluice, boom, and 
hydraulic have been successively adopted in al¬ 
most every gravel-mining district in America. 
Unfortunately, exact records of the possible work 
with each are almost unattainable, and, even if 
they were, variations in the character of the 
gravel would to a large extent nullify their 
value. The following comparative table, giving 
figures of work performed, first, on ordinary 
gravel, which is quite tractable, and, second, on 
cemented gravel, which is perhaps the most re¬ 
fractory known, will perhaps be of value to the 

19 




20 


HYDRAULIC MINING. 


miner. The two may be regarded as extremes. 
The table shows the number of cubic yards of 
dirt which may be washed per day of 10 hours 
per man—in the first two cases each man work¬ 
ing alone, and in the last four in pairs, or 
economically-arranged gangs: 


Ordinai'y. Cemented. 

By the pan._ 1 cu. yd. feu. yd. 

“ rocker. 2 “ 2 “ 

long tom... 5 to 6 “ 3 to 5 “ 

“ sluice. 10 to 20 “ Gtol2 “ 

“ hydraulic.. 100 to 1000 “ 100 to 1000 “ 

boom. unlimited. unlimited. 


It will be understood by every miner that no 
exact figures can be given in a comparison of 
this nature, and that the character of the 
ground will very largely affect the amount of 
work done. With the pan, which will hold 
from fifteen to thirty pounds of gravel, only 
a very little ground can be washed under any 
circumstances. If the ground abounds in large 
boulders which can be removed by the hand 
with ease, a miner will wash twice as much as 
otherwise. One hundred pans are considered as 
a good day’s work for a careful operator. The 






HYDRAULIC MINING. 


21 


same consideration—that of boulders—applies 
to the work in a rocker and long tom. The 
latter permits a more easy and thorough break¬ 
ing up of cement, and the water generally 
being supplied automatically, it is operated at 
a smaller cost. But neither aro adapted for 
operations on a large scale, nor in any ground 
carrying less than three to five dollars per 
yard. 

The ground-sluice is a device which com¬ 
mends itself for banks not too high to cause 
danger from caving, and when a good grade 
in the pit can be obtained. The unfavorable 
point in this system lies in the fact that all 
boulders must be moved twice, and that no 
clean-up can be made till the end of the sea¬ 
son. In consequence, either the work is pro¬ 
longed, with great discomfort to the men, into 
the period of cold weather, or much water is 
allowed perforce to run to waste. 

Where extensive operations are contemplat¬ 
ed the miner has to decide between the boom 
and hydraulic, or a favorable combination of 
the two. In California the boom is wholly 


22 


HYDRA ULIC MINING. 


abandoned in favor of tin? hydraulic, and in 
Colorado it is rapidly being superseded. Yet, 
as a system of placer-mining, it has many 
strong recommendations, and, according to 
some of the best Colorado authorities, is often 
the superior method. It seems to possess most 
merits when either the water is very abundant 
or very scarce. 

The boom will undoubtedly cave more ground 
per day and at a less cost than the hydraulic, 
unless it is a very hard cement. In its opera¬ 
tion it is the counterpart of the work of nature 
in natural ravines. For the purpose of clean¬ 
ing off top dirt of poor quality it has no supe¬ 
rior, and for ground carrying no leaf-gold it is 
claimed by some to be greatly preferable. Much 
depends upon the sluice and the manner of 
operating it. 

But where the ground is hard and force is 
necessary to tear it to pieces, where the banks 
are low and the gravel tenacious, the hydraulic 
is, by the testimony of most practical miners, 
the most advantageous. In many cases the two 
can be combined with most beneficial results. 






HYDRA ULIC MIRING. 


23 


In deciding which plan to adopt the miner will 
do well to bear in mind the principle that he 
is working, as a first consideration, to make 
money—not only to tear away the largest pos¬ 
sible amount of gravel. Consequently, that 
method or combination of methods is the cor¬ 
rect one which will deliver the largest quantity 
of gravel (with its gold) at his head box in the 
shortest time—provided always that he has 
sluice capacity and water sufficient to wash it 
thoroughly. 

In nine cases out of ten the method to be 
adopted is decided by the amount of water 
available ; and if the supply is unlimited (which 
is very rarely the case) the hydraulic is always 
better than the boom, if the two cannot bo used. 
The quantity of work possible to be done with 
the hydraulic varies, of course, with the nature 
of the gravel, the size of the stream, and the 
head. A very sound practical authority gives 
the following rough estimates : 

No. 1 nozzle, supplied with 100 miners’ inches 
of water, under a head of 100 feet, assisted by a 


24 


HYDRAULIC MINING . 


ground-sluice of 100 inches, will wash 600 cubic 
yards per day ; 3 men. 

No. 4 nozzle, supplied with 700 inches, under 
a head of 150 feet, will wash 3,000 cubic yards 
per day ; 4 men. 




CHAPTER III. 

i 

DIRECTIONS FOR THE MINER. 

I attempt in this work to give rules and di¬ 
rections for solving all the simpler engineering 
problems which the practical hydraulic miner 
(who in most cases is unacquainted with higher 
mathematics) will have presented to him. To 
be successful the miner must make himself 
thoroughly acquainted with the contents of this 
chapter, which is intended to be explanatory of 
such mathematical operations as will be noted. 
He who is able to add, subtract, multiply, and 
divide will find nothing in this book beyond 
his ability, if this chapter is carefully studied, 
and if the same hard common sense and intel¬ 
ligence which in all other matters distinguishes 

the American miner from other classes of work- 

25 






26 


HYDRAULIC MINING . 


ingmen is brought to boar on the subject. Hy¬ 
draulic mining is a branch of engineering, and 
because its operations can be guided wholly by 
mathematical rules it presents so much of cer¬ 
tainty and so little of risk. Consequently, the 
miner who desires to improve his property and 
increase his profits, but is unable from various 
causes to obtain the assistance of an experi¬ 
enced engineer, will certainly find it to be 
worth his while to gain the power of solving, 
alone and unaided, a majority of the problems 
which will be presented for consideration in 
the ordinary course of his business. 

I will call the reader’s attention, therefore, to 
the following subjects : 

1. The use of decimals ; 

2. The method of transforming fractions into 
decimals ; and, 

3. The principle of expressing the terms of a 
problem in a uniform and correct manner. 

DECIMALS. 

The decimal system is a method of numerical 
expression based upon a division of the unit 






HYDRAULIC MINING. 


27 


one (1) by ten (10) or multiples of ten (as, 100, 
1,000, 10,000). For example, instead of say¬ 
ing one-half (-|) say five-tenths ( T 5 ¥ ), and instead 
of saying one-quarter Q-) say twenty-five one- 
hundredths (y/o-)- The system, however, does 
not stop here, but includes a system of nota¬ 
tion which does away completely with the form 
of the fraction—thus : 


5 

10 

is written 

.5 

25 V 

10 0 

(( 

.25 

-84 _ 

10 0 

a 

.84 

__i2_ 

TIT 0 0 

u 

.012 

61JL 

To 0 0 

a 

.611 

92 6 2_ 

1 0 0 0 0 

a 

.9262 

14 

100000 

(t 

.00014 


lienee, to write down a decimal fraction deci¬ 
mally, follow this rule : 

1. Replace the figure 1, which is always the 
first figure of the lower part of the fraction, by a 
dot (.). 

2. Rub out as many of the last figures of 
the lower part of the fraction as there are 




28 


HYDRAULIC MOVING. 


figures in the upper part, and place these figures 
in the room of the figures rubbed out. 

For instance, to express decimally the frac¬ 
tion four hundred and eleven ten-millionths 



Replacing the 1 by a dot, we have .0000000. 
Second, as there are three figures in the upper 
part of the fraction, we rub out the last three 
ciphers of the above, and rejdace them with 411, 


making 


.0000411 


Again, express decimally three hundred and 
one thousandths (yWo). 


Replacing the 1 by a dot gives 
and placing in the 801 gives 


.000 

.301 


Again, express thirty-two tenths (ff). This 
fraction is evidently the same as three and two- 
tenths (3 T 2 y), which, treated by the rule, gives 3.2. 

The addition of decimals is performed exactly 
as any other addition. Place the two or more 
quantities under each other, taking care that the 
decimal-points, the dots (.), are in a line, and 
place the decimal-point in the answer or result 
in the same position, thus: 






HYDRAULIC MINING. 


2 9 


.0104 

3.26 

.192 

114. 

117.4624 

In subtracting adopt precisely the same 
course, thus: 

1.242 

.012 


1.230 

.61306 

.4 

.21306 

In multiplying place the quantities in the or¬ 
dinary way, multiply as usual, and point off as 
many figures in the result as there are decimals 
in the two quantities multiplied, thus: 

1.264 

.06 


.07584 







30 


HYDRAULIC MINING . 


Again: 

.1103 

.17014 

4412 

1103 

7721 

1103 

.018766442 

The division of decimals is performed as fol¬ 
lows : 

Set down the figures as in the ordinary style 
of long division. Annex to the dividend (the 
quantity to be divided) first as many ciphers as 
may be necessary to make the number of deci¬ 
mal figures in the dividend equal in number to 
those in the divisor, and, second, as many more 
as may be necessary to obtain a figure large 
enough to divide. 

Divide as in the ordinary method. 

Point off in the result as many places for de¬ 
cimals as the number of decimals in the dividend 
exceeds those in the divisor. 






HYDRA ULIC MINING. 


31 


Note.— If the divisor or dividend consists of 
decimals commencing with a cipher or several 
ciphers (as, .0218 or .00014), these ciphers may be 
wholly disregarded in the operation of division. 

The following examples cover all cases : 

(a) When the divisor is larger than the divi¬ 
dend—as, to divide 1.265 into .04: 

1.265).04000000(3162 
3795 


2050 

1265 


7850 

7590 


2600 

2530 


In this case, there being 8 decimals in the di¬ 
vidend and 3 in the divisor, the difference 5 will 
he the correct number for the quotient or an¬ 
swer, which, instead of being 3162, will be .03162. 






32 


HYDRA ULIC MINING. 


(b) When the divisor is less than the dividend— 
as, to divide .142 into 4.G: 

.142)4.000(32 

426 

340 

284 

There being an equal number of decimals in 
both divisor and dividend in this case, the quo¬ 
tient remains unaltered as 32. But if, instead of 
annexing two ciphers, we had annexed, say, six, 
the quotient would have been 323943, we would 
have had four more decimals in the dividend than 
in the divisor, hence the result would have been 
- 32.3943. 

In the division of decimals, ciphers may be an¬ 
nexed to any extent desirable until no remainder 
occurs; this makes the division perfect. Other¬ 
wise it is an approximation. But in all calcula¬ 
tions except those of a most delicat*e nature it is 
sufficiently accurate to annex only enough ci¬ 
phers to produce three decimal figures in the 
result. 






HYDRAULIC MIXING. 


33 


(c) Where ciphers are prefixed to dividend or 
divisor, or both, a study of the following opera¬ 
tion will explain the method. Thus, to divide 
.0014 into .0000403 : 

.0014).0000403(28 
28 

123 

112 


There being 7 decimals in the dividend and 
4 in the divisor, the answer should contain the 
difference, or 3 figures, giving, in place of 28, 
the quantity .028. 


TRANSFORMATION OF FRACTIONS INTO 

DECIMALS. 

When a problem under consideration contains 
fractions it is always necessary to reduce these 
to decimals. This is done by simply dividing 
the numerator of the fraction (the top figure) 
by the denominator (the bottom figure). Thus, 
to reduce 4 to decimals divide 1 by 2 = .5 ; or to 
reduce -§, divide 3 by 8=.37o ; or to reduce f, 






34 


HYDRA ULIC MINING. 


divide 3 by 4=.75. The division need not be 
carried to more than three figures. 

This must be done in all cases. As an exam¬ 
ple, if the grade of a flume is found by experi¬ 
ment to be inches per box, the fraction is 
to be reduced to decimals by dividing 5 by 12, 
thus : 

12)5.000(416 

48 

20 

12 

80 

72 

Pointing off the result (416) according to the 
rule of division of decimals, the grade is found 
to be 3.416 inches per box. 

THE PRINCIPLE OF EXPRESSING TIIE TERMS OF 
A PROBLEM UNIFORMLY. 

At the beginning of a problem it is necessary 
to reduce all the elements to the right shape and 
form. If this is done confusion will be avoided. 


HYDRAULIC MINING. ' 35 

If it is not done the results will be false almost 
invariably. Hence, 

Express perimeter, lengths of flumes, ditches, 
piping, head, diameters, etc., in linear feet and 
decimals of a foot. 

Express areas (such as sections of flumes and 
piping, and mouths of nozzles) in square feet 
and decimals of a foot. 

Express discharge in cubic feet per second. 

Express velocity in linear feet per second. 

Express grade in decimals of a foot per linear 
foot. 

Thus, discharge from a flume or pipe, which 
is frequently given in miners’ inches, should be 
reduced to cubic feet (see Miner’s Inch) ; grade, 
which is generally expressed in inches per box 
(12 feet) or inches per rod (16 feet), must inva¬ 
riably be altered to feet per foot; as, for in¬ 
stance, a grade of 1 inch per box equals 1 inch 
per 12 feet, or ^ of an inch per 1 foot. But 
of an inch equals of a foot, which, reduced 
to decimals, equals .007 of a foot nearly. The 
correct mode of expression, therefore, will be 
.007 feet per foot. 


3 6 


HYDRAULIC MINING. 


Velocity must be expressed in feet per second, 
and perimeters in decimals of a foot. A liume 
having a perimeter of 20 inches measures If of 
a foot. Reducing this to decimals, we have, in 
place of 20 inches, 1.666 feet. 

DEFINITIONS. 

The subjoined definitions and explanations 
will be found necessary to a perfect understand¬ 
ing of the technical phrases used in succeeding 
pages. The reader is therefore invited to im¬ 
press on his mind the exact meaning and value 
of each term defined: 

Mass .—The quantity of matter which a body 
contains—irrespective of whether that quantity 
be diffused through a large space, through the 
influence, for example, of heat (as in the case 
of steam) ; or compressed inJo a small space, 
through the influence, for example, of cold (as 
in the case of ice)—is called its mass. 

Volume .—The amount of space occuqyied by a 
body is denominated its volume. 

Weight .—When a body is freely acted upon by 
gravity, but is prevented from moving by some 


HYDRAULIC MINING. 


37 


supporting obstacle, the 'pressure on the point 
of support is termed its weight. 

Jet. —A jet is the mass of water escaping from 
a vessel through an orifice in its side or bottom, 
which orifice, of course, must be below ilie level 
of the water. 

Flow .—The volume of water which escapes 
from a vessel through an orifice (which may be 
wholly or partly under the water) in any given 
time is its flow for that time. 

Velocity. —The distance passed over by any 
given mass of water in any given time is called 
its velocity. The direction of the motion is 
immaterial. 

Head .—The vertical distance between the level 
of standing water in a reservoir, and the centre 
of the orifice from which it flows into the air, 
is called its head. 

Wet Perimeter .—If a flume or ditch is 20 
inches wide, 6 inches deep, and full of water, 
its wet perimeter is 20-J-G-f-6=32 inches. If 
of the same dimensions, but only containing 
3 inches of water, the wet perimeter is 20+3 
+3=26 inches. The same flume again, if 



38 


HYDRAULIC MINING. 


empty, has no wet perimeter at all. In other 
words, the wet perimeter of a water-channel is 
the length of so much of its base and sides as is 
wetted by the water. This measurement deter¬ 
mines friction. 

Friction .—Wh'en one body is slid upon an¬ 
other, the inequalities and roughnesses of the 
two surfaces interlock and cause a resistance, 
which is termed friction. If, now, the sliding 
body has not sufficient weight and cohesion to 
create abrasion or wear among these irregulari- 
ties and roughnesses, the degree of friction which 
arises bears a well-known proportion to the 
weight of the sliding bod} 7 . This is the case 
when water slides along the floor of a flume or 
ditch, and the proportion of friction developed 
to the weight of the water is called 

TIIE CO-EFFICIENT OF FRICTION. 

This co-efficient, of course, varies as the water 
is muddy or clear, or as the flume floor is rough 
or smooth. It is however, wholly independent 
of the areas of the surfaces in contact. In other 
words, two flumes of different size, if made of 


HYDRA ULIC MINING. 


39 


the same quality of lumber and carrying similar 
water, will develop identical co-efficients of fric¬ 
tion—the proportion of friction to the moving 
weights will be the same. But the weights of 
water in each being different, the amount of fric¬ 
tion developed in the larger flume will be greater 
than in the smaller. 

Momentum .—The quantity of force which a 
body in motion is capable of exerting when 
stopped suddenly is called its momentum. Proba¬ 
bly the best illustration of this is the power ex¬ 
hibited by a jet of water when it strikes a bank 
of gravel. It may be measured by multiplying 
the weight of the striking body by the velocity 
at which it moves. For example: A nozzle de¬ 
livering a stream of water 3 inches in diameter, 
with a velocity of 150 feet per second, will hurl 
against a bank every second a force equal to the 
weight of a column of water 3 inches in diame¬ 
ter and 150 feet high, multiplied by 150, or 34^ 
tons nearly. But it is to be remembered that 
this is the amount of force developed at the 
mouth of the nozzle only. Immediately on 
passing into the air the stream of water-, acted 


40 


HYDRAULIC MINING. 


upon by the force of gravity and the resistance 
of the air, and further weakened through its own 
disintegration, becomes less powerful. At a suf¬ 
ficiently great distance from the mouth of the 
nozzle the velocity will be wholly lost, and no 
force or power remains except that due to the 
weight of each particle of water under the influ¬ 
ence of gravity. Again, it is not to be thought 
that if a gravel-bank is struck with the force 
above mentioned 34£- tons of earth must be 
moved per second. This statement appears to 
be unnecessary, though it may be logically de¬ 
duced from the first, unless it be remembered 
that vast quantities of force must be expended 
in destroying the cohesion of the gravel and 
overcoming its inertia. Once in a state of mo¬ 
tion, the force transmitted from the nozzle to 
the gravel would, if the force could be applied 

at a point which would equally affect the whole, 

* 

give it as rapid motion as the water, less fric¬ 
tion. But this can never be accomplished in 
practice. 

MENSURATION. 

A few questions in mensuration will arise in 


HYDRAULIC MINING . 


41 


working the problems presented in the following 
pages. These are as follows : 

1. To find the Area of a Circle. —Multiply 
the diameter (in inches) by the decimal 3.14 
and the product by one-quarter of the diameter. 
The result will be the area in square inches. 

9 

Divide this by 144, and the result will be the 
area in square feet. 

Example.— What is the area of a circle 16 
inches in diameter'? 

16 multiplied by 3.14=50.24 multiplied by 4 
(which is one-quarter of the diameter) = 200.96 
square inches, which divided by 144=1.32 square 
feet. 

2. To find the Area of a Section of a Flume 
with Straight Sides. —Multiply the width of 
bottom (in inches) by the height of sides (in 
inches); the product will be the area in square 
inches, which, divided by 144, gives the area in 
square feet. 

Example.—W hat is the area of a section of a 
Hume 20 inches wide and 15 inches high ? 

20 multiplied by 15=300, which divided by 
144 = 2.08 square feet. 


4 2 


HYDRAULIC MINING. 


3. To find the Area of the Section of a Ditch 
with Sloping Sides. —Add together the width at 
top and bottom (in inches), multiply this sum 
by the depth (in inches), and divide the result 
by 2. The quotient, divided by 144, will be the 
area in square feet. 

Example.— What is the area of the cross-sec¬ 
tion of a ditch GO inches wide at the top, 36 
inches at the bottom, and 12 inches deep ? 

60 plus 3G = 96, which multiplied by 12 = 1152, 
and this divided by 2 = 576 square inches, which 
divided by 144=4 square feet. 

4. To find the Area of the Cross-Section of a 
Ditch whose Sides slope to a Point at the Bot¬ 
tom. —Multiply the width (in inches) by half 
the depth (in inches), and divide the product 
by 144. The result is the area in square inches. 

Example.— What is the area of a pointed 
ditch GO inches wide and 18 inches deep in the 
centre ? 

60 multiplied by 9 (half the depth) = 540 
square inches, which divided by 144=3.75 
square feet. 




CHAPTER IV. 


THE PROPERTIES OF WATER. 

In hydraulic mining the properties of water 
are to be considered in but two conditions: 

(a) When at rest—as in the case of dams, re¬ 
taining walls, and pressure-boxes ; and 

(k) When in motion—as in ditches and 
flumes. 

WATER AT REST. 

The three principles here laid down will be 
worth consideration by the miner who desires to 
work understandingly. 

1. Water at Rest transmits Pressure equally 
in all Directions .—If a pressure of 100 lbs. is 
exerted on the entire surface of the water in a 
reservoir whose section is 10 square feet, this 
pressure is transmitted in its entirety not only 
to the base, but to every 10 square feet of its 
sides. Thus, if the interior surface of the reser- 

43 


44 


HYDRAULIC MIXING. 


voir (base and sides) measures 250 square feet, 
and a pressure of 100 lbs. is placed on the water- 
surface (of 10 square feet), the base and walls 
will receive a total pressure of 2,500 lbs. Or if 
the box be so closed at the top as to leave but 
one square foot of water exposed, and if a pres¬ 
sure of 100 lbs. be applied on this one square 
foot, an equal pressure will be transmitted to 
every square foot of interior surface, and the 
total will consequently be 25,000 lbs. Or, to 
illustrate this remarkable property still more 
thoroughly, suppose the top of the vessel to be 
covered with the exception of one square inch. 
If on this a pressure of 100 lbs. is placed, every 
square inch of interior surface will be pressed 
outward with this weight, which, for the size 
box under consideration, would amount alto¬ 
gether to 1,800 tons. 

This is the principle utilized in the hydraulic 
press. 

2. The Pressure exerted by Water on the 
Horizontal Bottom of a Vessel is wholly inde¬ 
pendent of the shape of the vessel, and is equal 
to the weight of a column of water whose base is 



in DRAULIC MINING. 


45 


the area of the horizontal bottom, and whose 
height is equal to the depth of the liquid. 

3. The Pressure of Water on the sides of a 
Vessel is equal to the weight of a column of 
water whose base is equal to the area of the side, 
and whose height is equal to one-half the depth 
of the liquid. 

Owing to this law the pressure on the walls 
and base of a cubical vessel is equal to three 
times the weight of the water contained. 

The two principal problems in hydraulic min¬ 
ing arising under the head of water at rest are 
those connected with the construction of dams 
and reservoirs and water-boxes. 

Referring to the third principle just enun¬ 
ciated, it will be seen that the pressure on any 
surface under water depends upon two things— 
the depth of water and the area of the surface 
pressed. For example, what will be the pres¬ 
sure against the inner slope of a dam 50 feet 
long, 12 feet wide, and 12 feet deep at the bot¬ 
tom ? Multiply the area of the slope (50x12 = 
600) by the average vertical depth in feet of the 
centre of gravity of the slope (6)=3,600, and 


46 


HYDRAULIC MINING. 


multi j)ly this by G2.5 (the weight of a cubic foot 
of water) =225,000 lbs. 

It will be noted that the pressure is not a 
pound greater if the water reaches back from the 
face of the dam for miles, than if it were a reser¬ 
voir only a few feet broad. Hence, if a reservoir 
is built simply for storage, make it large and 
shallow rather than small of area and deep. 
The loss by solar evaporation will, it is true, be 
much greater, but this disadvantage will be 
counterbalanced, first, by the small leakage; 
second, by the cheapness of the dam ; and, third, 
by the great safety of the construction. A 
miner cannot go to his work under more de¬ 
pressing circumstances than with the thought 
that at the head of the gulch in which he is im¬ 
prisoned is a dam whose embankment of 15 or 
20 feet in height may at any time give way and 
destroy not only himself and comrades, but 
every trace of improvements that have been the 
labor of years. 

Probably the best and safest embankment, 
where there is no carpentry or masonry, is that 
one which is modelled on the plan of the beaver- 



HYDRAULIC MINING. 


47 


dam. This is a familiar sight in the West, and 
its details can be easily studied. The beaver- 
dam is seldom if ever known to give way, and 
this quality of stability is what is of all things 
most desirable. 

The water or pressure box has three uses. It 
determines permanent and steady head ; it offers 
an opportunity to clear the water from gravel 
and other debris before passing it into the pipe, 
and it should be the means of freeing it from a 
large portion of the air which it absorbs while 
travelling at a high velocity. 

Construction .—The pre sure-box should be a 
deep vessel, with a pyramidal bottom pointing 
downward and provided with a trap. This, on 
being opened from time to time, will clear out 
gravel and sand which has collected in the bot¬ 
tom, and which, if allowed to accumulate, would 
in time rise to the level of the outflow. The 
pressure-box is best built when its height, ex¬ 
clusive of pyramidal bottom, is three times its 
greatest width. The section should be longer 
one way than another. It should have a lip 
overflow on one of the short sides, and the water 


48 


HYDRA ULIC MINING. 


should enter the box at the centre of its top, 
and from the same side as the discharging-lip. 
All screening should be done in the flume. A 
partition reaching down below the outflow, and 
parallel with the longest sides, is highly recom¬ 
mended by good authorities. The discharge- 
hole should be two-thirds of the distance from 
top to bottom (no increase of power is gained by 
placing it at the bottom), and should be in one 
of the long sides. If these directions are ob¬ 
served a large quantity of the gravel unavoidably 
carried into the box will be prevented from pass¬ 
ing into the pipe, much of the air will also be 
kept out, and a steady and even head will be se¬ 
cured. 

We have now to consider only the strength of 
the box. That this is an important point may 
be judged by the fact that if its height is 12 feet, 
and its section 3 by 4 feet, it will have to sustain 
a pressure of not less than 35 tons. 

MEASURING THE WATER OF STREAMS. 

If the channel of the stream has a moderately 
even outline, measure its depth at regular in- 



IIYDRA ULIC MINING 


49 


tervals from shore to shore. Add all these 
depths together, and divide the sum by the 
number of soundings. An average depth is thus 
gained. Calculate then the area of the section 
according to Rule 2, page 41. Measure the velo¬ 
city by means of a float, and make the test about 
half-way between the bank and the centre. Mul¬ 
tiply the area by the velocity, and the product 
will be the flow. Of course the test for velocity 
should be made at the same point where the 
measurements for depth are made, and a place 
on the stream should be selected for both where 
the banks are as nearly parallel as may be, and 
where the current and flow is the most tranquil. 

Example. —A stream is 24 feet broad, and ten 
soundings at every two feet on a line from bank 
to bank give 2, 6, 8, 9, 7, 11, 11, 10, 9, and 2 
inches as the depths. The average velocity as 
determined by float is 4 feet per second. What 
is the flow ? 

The sum of the 10 soundings is 75 inches, 
which gives an average depth of 7.5 inches, 
equal to .025 of a foot. The area of the section, 
then is 24 multiplied by .025=15 square feet. 


50 


HYDRAULIC MINING. 


The velocity being 4 feet per second, the flow is 
equal to 15 multiplied by 4=GO cubic feet per 
second. 

If the stream runs over a bottom so irregular 
that an average depth cannot be gained or an 
average velocity measured, there is no recourse 
but to construct an artificial channel having no 
grade, into which it may be turned while mea¬ 
sures are made. The same rule applies in this 
case as before, and it should be understood that 
in both the results are very rough approxima¬ 
tions. To reduce the result to miners’ inches 
refer to the table of equalities, page 18. 


CHAPTER Y. 


CONSTRUCTION OF WATER-WAYS. 

When the miner has measured the stream 
from which he is to draw his water-supply, and 
has determined that point where he will tap it, 
he is prepared to consider the question of water- 
channels. These may be of three kinds—the 
ditch, the wooden flume, and the iron pipe. The 
ditch is the most indestructible, the cheapest, 
and the easiest to repair. Instead of deteriorat¬ 
ing, it improves in condition year by year if 
carefully built. On the other hand, more water 
is lost by evaporation, and in stormy seasons it is 
subject to injury by overflows, land-slides, caves, 
etc., etc. The wooden flume eliminates the ele¬ 
ment of loss by leakage, but not by evaporation. 
It occupies the middle ground in point of cost, 
but requires much watching. It is, moreover, 
the most easily destroyed by fire and flood. The 
iron pipe prevents all loss on the way, is most 

51 




52 


HYDRAULIC MINING. 


easily cared for, and costs the most. It is seldom 
considered to be the best method of water trans¬ 
portation, except when a necessity, as in the case 
of siphon-bends or very steep grades, or on the 
rocky side of mountains where ditching would 
be costly. 

It is generally desirable to have the least pos¬ 
sible fall in a water channel, or. in other words, 
to bring the water to as high a point of the 
ground to be worked as circumstances will allow. 
As the friction of the sides and bottom of a 
channel retards the flow, and necessitates a high¬ 
er grade than would be necessary if there were 
none, it becomes of importance to decrease this 
element as much as possible. On this score 
wood and iron water-ways present decided ad¬ 
vantages, owing to their comparative smooth¬ 
ness. In any case, however, the quantity of 
friction developed depends upon the wet perime¬ 
ter of the channel used. The following law will 
therefore be found of service : 

The least wet perimeter that will hold or carry 
a given volume is attained when the width of lot- 
tom is from If to 2f times the depth of the sides. 


HYDRAULIC MINING. 


53 


For example, a channel having a cross-section 
of 510 square inches will develop the least amount 
of friction when its dimensions are 15 by 3-4, or 
17 by 30, or somewhere between these measure¬ 
ments. 

A knowledge of this fact will he found ser¬ 
viceable in constructing flumes. The least peri¬ 
meter, of course, requires the least lumber, and 
many thousand or million feet may be saved in 
a long flume by building in the correct pro¬ 
portion. 

When the head of the flume is above timber- 
line, or in high altitudes where ice forms early in 
the fall, it is an advantage in many respects to 
have it so narrow in width that an ice-crust can 
easily form itself from bank to bank. If this is 
secured water will often flow a month or six 
weeks longer than otherwise. The reasons are 
obvious. 

In making the preliminary survey of a placer- 
claim a sound authority advises as follows: First, 
lay off the dump ; second, decide how much 
grade and fall to give the sluices ; and, third, 
find the least fall necessary between source of 


54 


HYDRAULIC MINING. 


water and water-box. The remaining distance 
will then be the greatest head attainable. The 
suggestion is pertinent, because it brings to mind 
the fact that a good dump and an abundant 
grade for sluices are fully as necessary for econo¬ 
mical gravel-washing as a heavy head of water. 

When the linear distance between the sources 
of supply and the water-box is determined, and 
the least fall that will carry the water ascer¬ 
tained (after considering the questions of fric¬ 
tion, evaporation, and leakage), the grade per 
foot is found by dividing the total fall in feet by 
the total length in feet. Multiplying the result 
(which will generally be a decimal) by 100 or 
1,000 will give the grade per 100 or 1,000 feet. 
Having now the grade per foot and the quantity 
of water to be carried (as determined by gaug¬ 
ing the stream or streams tapped by the ditch or 
flume—the proper deductions having been made 
for leakage and evaporation), the area of cross- 
section of the water-way may be determined by 
the rule for the determination of the least wet 
perimeter, which has just been given. 

Solar evaporation is very active at high alti- 


HYDRAULIC MINING. 


* p» 

33 

tudes. The ordinary figures representing loss 
through evaporation (Jy- to T 3 ¥ of an inch of sur¬ 
face per day) are much too small for ditches 
above an altitude of G,000 feet. Evaporation 
also proceeds much more rapidly in shallow water 
than in deep, and when the velocity is high. 
Experiments made during 1877 on the 12-mile 
wooden flume of the Fuller Company, on the 
Swan River, Colorado, indicated a loss of from 
10 to 18 per cent, daily. This flume is, how¬ 
ever, an extreme case, being about 10,000 feet 
above sea-level. Probably an inch of surface 
would be an average loss. 

Leakage occurs most extensively in gravelly 
soils. From 1 to 5 inches of surface per day 
are extreme losses, with an average, perhaps, of 
about 2 inches, which it will be always safe to 
count on, except in old ditches. A high velo¬ 
city decreases loss through the soil. 

Water-channels of uniform section should al¬ 
ways have a uniform grade. Otherwise there will 
be an accumulation in some points and a tliin- 
ning-out in others, with deposits of sand and 
silt in the latter case, and in each case with in- 



56 


HYDRAULIC MINING. 


creased danger of breakage. It will also be 
found highly advantageous in earth ditches to 
have a complete system of waste-weirs to carry off 
surplus waters occasioned by floods and to lessen 
the damage of breaks. These should be put in 
just below wherever a new stream falls into the 
ditch, and just above those places where, by rea¬ 
son of a shelly or crumbly soil, the ditch is weak. 
A break is bad, not only because it must be re¬ 
paired, but because while being mended all min¬ 
ing operations must cease. 

In the spring, difficulty is often encountered 
in starting the water through the heavy accumu¬ 
lation of snow in the ditch, which, if it be long, 
can be flushed out only with great trouble. 
This operation will be materially hastened if the 
ditch is cleaned out in short sections of a mile or 
two each. Cut a hole in the bank a mile from 
the head, and when the water has soaked that 
far it will carry off the unmelted snow through 
this break with great rapidity. As soon as clear 
the hole is mended and another made a mile 
further on. Time will be saved by thus taking 
the ditch in sections. 


HYDRAULIC MINING. 


57 


Cost .—When the plough and scraper can be 
used ditching can be done at 20 cents per cubic 
yard. If the soil is so rocky as to call for the 
pick and shovel, it will cost from 30 to 40 cents. 
A safe figure to be taken for the construction of 

i 

a ditch 3 feet wide at bottom, 4£ feet wide at 
top, and 18 inches deep is $1 25 per rod. It 
can be done for less. The larger the ditch the 
less costly it will be in proportion. 



CHAPTER VI. 


FLOW OF WATER IN FLUMES AND DITCHES . 

The following rules for the solution of prob¬ 
lems concerning the How of water in ditches and 
Humes are commended to the miner, only with 
the proviso that the directions laid down in 
Chapter V he strictly complied with. Before 
doing any figuring let every element of the prob¬ 
lem, as grade, area of section, velocity, wet peri¬ 
meter, discharge, and length, be reduced from 
the ordinary measurements usually given to 
those laid down in the “Directions.” If this is 
done the results may be depended upon; other¬ 
wise they will be of no value. 

It is to be remembered, however, that these 
rules do not take into account leakage and 
evaporation—two elements of loss which have 
been spoken of already. It will be impracticable 
in this manual to enter into the details of these 
elements of loss, as the subjects are too intri- 

58 


HYDRAULIC MINING. 


59 


cate; and, in addition, it would be unnecessary, 
inasmuch as the records of experience are more 
satisfactory and nearer the truth. 

1. What grade per foot must he given to a 
flume or ditch of uniform section to enable it to 
discharge a given quantity of water in a given 
time ? 

Rule 1 . Divide the number of cubic feet of 
discharge required by the area in square feet of 
the section of the flume. This result is the 
velocity necessary, expressed in feet per second. 

Multiply this result by itself. 

Multiply this product by the wet perimeter, 
expressed in feet, and multiply this product by 
the decimal .0001114. * 

Divide this product by the area of the section 
of flume, expressed in square feet. Call the re¬ 
sult A. 

Multiply the velocity in feet per second by the 
wet perimeter, expressed in feet, and multiply 
this product by the decimal .00002420. 

Divide this product by the area of the section 
of the flume, expressed in square feet. Call the 
quotient B. 





6o 


HYDRA ULIC MINING. 


Add together A and B. 

The result is the grade per foot (expressed in 
decimals of a foot) which must be given to the 
flume to make it carry the required water. 

Example.— What grade per foot of length 
must be given to a 20-inch flume whose sides are 
11 inches high, in order that it may deliver 28 
cubic feet of water per second steadily ? 

Wet perimeter, 42 inches = 3.5 feet. 

Area of section, 240 sq. inches= 1.66 sq. “ 

Discharge, =28.00 cubic “ 

Then, dividing the discharge (28) by the area 
of section (1.66), we have 16.86 as the velocity in 
feet per second. 

Foliowing^the rule, the velocity (16.86) multi¬ 
plied by itself equals 284.25 ; multiplying this 
by wet perimeter (3.5) produces 994.87; multi¬ 
plying again by the decimal .0001114 produces 
.1108 ; dividing this by area of section (1.66) 
gives .0667. Call this A. Multiplying the ve¬ 
locity (16.86) by wet perimeter (3.5), and the 
product by .00002426, produces .0014315, which 
divided by the area of the section of the flume 
(1.66) =.00086. Call this B. Adding A (.0667) 


HYDRA ULIC MINING. 


6l 


to B (.00086), we have as a final result .06756, 
which is the grade per foot (expressed in deci¬ 
mals of a foot). If we multiply this result 
(.00756) by 1,000, we have the grade per thou¬ 
sand feet, which will ho 67.5 feet (near enough). 

To reduce this result to the ordinary terms— 
viz., inches per box of 12 feet—divide first 1,000 
by 12, which produces 83.33 (which of course 
represents the number of 12-foot boxes in a 
1,000-foot flume). Then, the grade being 67.5 
feet in 83.33 boxes, for each box it would be the 
result of d viding 67.5 by 83.33, which is .79, or 
the grade would be .79 of a foot per box of 12 
feet. Finally, there being 12 inches in a foot, 
we multiply .79 by 12 and ob’ain 9.48 inches per 
box, or nearly 94 inches. 

2. What is the average velocity and discharge 
secured in a flume or ditch of uniform cross- 
section and grade ? 

Rule 2.-—Multiply area of cross-section in 
square feet by the grade in feet per foot, and the 
product by 9,000. 

Divide this result by the wet perimeter in 
feet. 




62 


HYDRAULIC MIXING. 


Extract the square root of the quotient. (See 
table at end of book.) 

From the result subtract .1089. 

The result equals the mean velocity of the 
water (expressed in feet per second). 

Multiply the area of cross-section by the mean 
velocity. 

The result equals the discharge (expressed in 
cubic feet per second). 

Example. —What is the discharge attained in 
a 30-inch-flume with 12-inch sides, having a 
uniform grade of (.01) of a foot for every 
foot of length ? 

Multiplying the area of cross-section (2.5 
square feet) by the grade (.01) produces .025 ; 
multiplying this by 9,000 yields 225 ; dividing 
this by the wet perimeter (4.5) gives 50, whose 
square root is 7.0111; subtracting from this the 
decimal .1089, we have G.9G22, which is the mean 
velocity (expressed in feet per second). 

This calculation is in reality accurate only for 
a flume. In a ditch, where friction is greater, it 
will be necessary to subtract about 10 per cent, 
(or .G962) from the result found, leaving 6.26G 


HYDRAULIC MIJV/NG. 


63 

as the correct figure. Then continuing, multi¬ 
ply the mean velocity (6.9622) by the area of 
cross-section (2.5) ; we have 17.40, which is the 
discharge (expressed in cubic feet per second). 

3. What must be the section of a ditch or 
flume of uniform grade which will discharge a 
given quantity of water in a given time ? 

There is no simple rule that will solve this 
problem, and ail answer must be sought experi¬ 
mentally upon the following plan : 

Rule 3. Assume a convenient section, and, the 
grade being known, calculate its discharge ac¬ 
cording to Rule 2, page 61. If this discharge is 
greater or less than the required one try again 
with a smaller or larger section until the correct 
one is found. 

Cost .—With lumber at $12 to $15 per thou¬ 
sand, delivered at the head of the flume, so that 
it can be floated down, a flume 2J feet wide and 
2\ feet high can be finished at a cost of $3.85 
per box (of 12 feet in length); and one 6 feet 
wide and 34 feet high at $8.50 per box. 



CHAPTER VII. 


IRON PIPING. 

The problems which arise in operating iron 
pipes are the following: 

1. What is the velocity attained in a cylindri¬ 
cal iron pipe, laid straight or with easy curves, 
its head, length, and diameter being known? 

Rule 1 . Multiply the diameter in feet by the 
head in feet. Call this product A. 

Add together the total length of pipe in feet, 
and 54 times its diameter in feet. Call this 
sum B. 

Divide A by B. 

Extract the square root of the quotient (see 
table at end of book) ; multiply this root by 48. 
The product will be the velocity in feet per 
second. 

Example. —What velocity will be attained in 
a pipe 12,000 feet long, 0 inches (.5 of a foot) in 
diameter, and having a head of 200 feet ? 



//} DRAULIC MINING . 


65 


Multiply diameter (.5) by head (200) =100; 
call this product A. Add to the total length 
(12,GOO ft.) 5-1 times its diameter: .5 multiplied 
by 54 equals 27=12,627. Call this sum B. Di¬ 
vide A (100) by B (12,G27) =.0070. Extract the 
square root of this resuB, which = .0889. Mul¬ 
tiply this root by 48 = 4.26, which is the velocity 
per second, in feet. 

2. How many cubic feet of icater per second 
will be discharged from a cylindrical iron pipe, 
straight or with easy curves, its head, length, 
and diameter being known ? 

Rule 2. Ascertain the velocity by preceding 
rule. Then multiply the velocity thus attained 
by the area in square feet of a section of the 
pipe. The result /will be the discharge per sec¬ 
ond, in cubic feet. 

3. What head of water' is. necessary for a 
cylindrical iron pipe, straight or with easy 
curves, its diameter and lenglh being known, 
to produce a given discharge per second ? 

Rule 3. Multiply the required discharge 
(expressed in cubic feet) by itself. Call this 
A. 


66 


HYDRAULIC MINING. 


To the total length of pipe add 54 times its 
diameter. Call this B. 

Multiply A by B. Call the product C. 

Divide the diameter (exjwessed in feet) by the 
decimal 235. 

Multiply this product by itself continuously 
four times. 

Divide C by this product. 

The quotient will be the head in feet. 

Example.— What head is necessary to pro¬ 
duce a discharge of 12 cubic feet per second at 
the end of a pipe 8 inches (.666 feet) in diame¬ 
ter and 350 feet long, the pipe being straight 
or with easy curves ? 

Multiply the discharge (12) by itself = J.44 ; 
call this A. To the total length (350) add 54 
times its diameter (36) =386 ; call this B. 
Multiply A (144) by B (386) =55,584 (C). Di¬ 
vide the diameter (.666) by .235=2.834. Mul¬ 
tiply this product (2.834) by itself continuously 
four times =182.801. Divide C (55,584) by this 
product (182.801) =304 feet nearly, which is the 
required head. 

4. What diameter of pipe is necessary to carry 



Ii YDRA ULIC MINING. - 6 / 

a given quantity of water per second, its length 
and total head being known ? 

Rule 4. Multiply the head in feet by 5,280, 
and divide the product by the length in feet. 
Call this A. 

Multiply the discharge in cubic feet per sec¬ 
ond by itself, and multiply this product by 
5,280. Call this B. 

Divide B by A. 

Extract the fifth root of the result (see tables 
at close of book). 

Multiply this by the decimal .235. 

The product is the diameter (in feet). 

Example.— What must be the diameter of a 
pipe 6,000 ft. long, with a head of 400 feet, 
which will discharge 6 cubic feet of water per 
second ? 

Multiply the head (400) by 5,280=2,112,000, 
and divide this product by the length (6,000) = 
352 (A). 

Multiply the discharge (6) by itself =36, flnd 
multiply this product by 5,280 = 190,080 (B). 

Divide B (190,080) by A (352) =540. 

Extract fifth root of this quotient (540) =3.52. 



68 


HYDRAULIC MIXING. 


Multiply this root (3.52) by .235 —.8272, which 
is the required diameter (expressed in decimals 
of a foot). 

Carves .—Curves and bends in pipes always 
cause some loss of power. They also furnish a 
place for the accumulation of air and sediment, 
as well as weaken the tube. They are, how¬ 
ever, unavoidable in practice, and the rules by 
which to calculate the additional amount of 
head necessary to counteract their influence, or 
the amount of power lost, are perhaps too com¬ 
plex for the aim of this work. An angular bend 
in a pipe should be avoided, if at all possible. 
In most placer districts there are workers of 
sheet-metal of sufficient ability to produce cir¬ 
cular elbows. The latter should be made with a 
radius never less than five times the length of 
their diameter. To ascertain this curve mea¬ 
sure the diameter of the pipe, and cut a string 
that will be just five times this length. Then 
if one end of the string be held fast the other 
will describe the correct curve. A still larger 
radius is better when possible. In fact, the 
gentler the curve the better. 






HYDRAULIC MINING. 


69 


Care should bo taken to back up piping very 
solidly at each change of direction. The neces¬ 
sity of this precaution will be self-evident. 
Cases have occurred where whole sections of 
piping poorly backed have been torn to pieces 
as soon as the head was put on. 

The cost of piping, finished and set up, may 
be approximated as follows : 


Cost at manufactory. 

4-1 c. per lb. 

Freight, 1,500 miles.. 

3^e. “ 

Making into pipe. 

3ic. 

Grading, laying, ballasting, and fas- 


tening. 



12c. per lb. 

The hydraulic grade-line is an imaginary 
straight line, extending from a point on the 
side of the water-box or reservoir, denominated 
the velocity-head, to the mouth of the nozzle. 
If the pipe be constructed exactly on this line, 
the water flowing through it, no matter what its 
velocity or volume, will exert no bursting pres¬ 
sure. I 11 other words, the grade of the hydraulic 
grade line is such that the velocity caused by the 
grade is exactly sufficient to carry down all that 




70 


HYDRAULIC MINING. 


the pipe will hold, and there is no outward pres¬ 
sure exerted except that on the bottom of the 
pipe due to the water’s weight. If, however, 
there he a change in the diameter of the pipe at 
any point this equilibrium ceases to exist. It is 
never possible in practice to adopt this line as a 
course, but generally close approximations can 
be made to it. As will be shown further on, it is 
highly advantageous to do this wherever possible. 

To find the Hi/draulic Grade-Line .— Rule 1. 
Calculate the velocity in qoipe due to the total 
head. (See Rule 2, page Gl.) 

Look in Table 3, and find the head correspond¬ 
ing to this velocity. 

Lav off this head on the side of the reservoir 

4/ 

from the top of the pipe-opening. Its termina¬ 
tion will mark the line of the velocity-head. 
From this point sight to the nozzle of the pipe ; 
the line of sight is the hydraulic grade-line. 

In constructing a line of piping three cases 
may arise by reason of the inequalities of the 
ground to be passed over : 

1. The pipe may lie below the hydraulic grade¬ 
line. 


HYDRA ULIC MINING. J I 

2. The pipe may lie above the hydraulic grade¬ 
line. 

3. The pipe may lie both above and below. 

Case 1. Pipe beloiv Hydraulic Grade-Line .— 

There is here a bursting pressure, varying in 
power according to its distance below the line. 
To find this pressure at any point, ascertain the 
distance of that p.unt vertically below the hy¬ 
draulic grade-line. Call this measurement the 

• 

bursting-head—as, for example, A, E, Fig. 1, 
which assume to be G feet. The pressure, then, 
on each square inch of pipe at that point is equal 
to the weight of a column of water whose base 
measures 1 square inch and whose height is 
6 feet. Thus, 1 square inch multiplied by G feet 
(72 inches) =72 cubic inches =.04166 cubic 
feet multiplied by G2.5 (wt. of cubic foot of 
water) =2.6 lbs., which is the pressure per 
square inch. Consequently, if the pipe lies con¬ 
siderably below the hydraulic grade-line, it will 
need to be of thicker iron than the rest. This 
law applies in crossing deep hollows. 

Case 2. Pipe above the Hydraulic Line .— 
There is now a decided loss of head, and conse- 


72 


II \ DR A ULIC MINING. 


quently of power, in portions of the pipe, if it be 
of the same diameter throughout. Find now 
that point in the pipe which is highest above 
the hydraulic grade-line (II), and from that 
point draw two new grade-lines, one to the 
pressure-box (II Y) and one to the nozzle (II 
N). Along the former calculate the bursting 
pressure as above, measuring the different heads 
from the new line (as F E). Along the latter 
there will be no bursting pressure, for the grade 
of the nozzle end of the pipe will be so much 
greater than that of the reservoir end that it will 
carry off the water very much faster, and will, in 
fact, act like a gutter, and be partially empty. 
The remedy for this is to put in pipes having a 
decreased diameter. To calculate the requisite 
diameter, assume that the pipe ended at that 
point where it is highest above the hydraulic 
grade-line (II). Calculate the discharge in cubic 
feet at that point according to Rule 2, page 61. 
This will give the amount of water in cubic feet 
per second which the nozzle section (II 1ST) must 
carry. The head will be the vertical distance 
from H to N. Then, by Rule 4, under the head 


HYDRAULIC MINING. 


73 

of Iron Piping, the requisite diameter may be 
calculated. 

Case 3. Pipe both above and beloiv the Hy¬ 
draulic Grade-Line .—*The problem now becomes 
more complicated. 

Divide the pipe into sections for every passage 
it makes above the hydraulic grade-line, and 
make the divisions at the several points (A, II, 
and I) where the pipe attains its highest posi¬ 
tion. Calculate (Rule 2, page Gl) the discharge 
at the end of each section. The first section 
will have a head equal to the vertical distance 
between its discharge and the water-level in the 
pressure-box. All succeeding heads will be 
measured from'the level of the discharge just 
below them to their own discharge. For ex¬ 
ample, the head at A is the vertical distance 
between A and the water-level in the reservoir. 
At II the head is the vertical distance between 
II and A. At I it is the distance between I 
and II, etc. These measurements will furnish 
a series of heads and grades from which the 
diameters of pipe necessary may be calculated 
according to Rule 4, page G6. 


74 


HYDRAULIC MINING. 


If it be desired to calculate bursting pressure 
in Case 3, measure the beads of different points 
from the new hydraulic grade-lines, and proceed 
as directed in Case 1. 

In building and laying lines of iron piping, 
■whether to conduct water from one reservoir to 
another or from the water-box to the pit, money 
will be saved by paying close attention to this 
subject. It will easily be seen that if the pipes 
are larger than is necessary, iron, which is gene¬ 
rally costly in mining communities, will be un¬ 
necessarily used, while at the same time the 
water will become filled with air, and much of 
its force thereby lost. Again, if the pipes are 
too small, the danger from bursting is greatly 
augmented. 

The pipe, after being laid, should be carefully 
anchored at every point, and, when possible, 
protected from the weather. 

The three conditions arising under unequal 
and varying grades are shown by the following 
figures: 


HYDRAULIC MINING . 


75 


Fig . 1 .—below Hydraulic Grade-Line. 

Fig. 1. 



W.—Water-box. F. E. N.—Line of Pipe. V. A. N.—Hydraulic 
Grade-Line. A. E.—Bursting-head. 


Fig. 2.—Pipe above Hydraulic Grade-Line. 



W.—Water-box. E. H. N.—Piping. V. N.—Hydraulic Grade-Line. 
F. E.—Bursting-head. V. H. and II. N.—Supplementary Hy¬ 
draulic Grade-Lines. 

Fig. 3 .—Pipe above and beloiv Hydraulic Grade- 

Line. 



W.—Water-box. A. E. II. F. I. N.—Piping. V. N.—Hydraulic 

Grade-Line. V A, A H, II I, I N—Supplementary Hydraulic 
Grade-Lines. 











76 


HYDRAULIC MINING. 




Sheet-iron, from which the piping is made, is 
manufactured of various thicknesses. The stan¬ 
dard of measurement is the inch, and a size 
known, for example, as No. 1G is T V of an inch 
in thickness. The following table will give the 
strength of sheet-iron piping, and will be found 
of service. 

STRENGTH OF IRON PIPING. 


This table gives the thickness in inches and decimals of an inch 
which iron piping mrst have to stand a given pressure. 


CO 

o 

v«* 

.g 

Si 

s* 

•to 

£ 

Head of Water, in feet. 

100 

150 

2 CO ! 

253 

300 ; 400 

1 

500 

GC0 

1 

800 

1,000 

Resulting Pressure against Sides of Pipe, in lbs. per sq 

inch. 

43.4 

1 

65.1 

87 

109 

130 174 

• 

217 

260 

347 

434 


Required III clcaess of Pipe, in inches or decimals of an inch. 

O 

.009 

.013 

.018 

.022 

.027 .036 

.045 

.055 

.075 

.095 

3 

.013 

.020 

026 

.033 

.040 1 .054 

.068 

.082 

.112 

.143 

4 

.017 

.026 

.035 

.045 

.053 .072 

.090 

.110, 

.149 

.191 

5 

.022 

.0 53 

.044 

.056 

.067 .090 

.113 

.137 

.186 

.237 

6 

.026 

.010 

.053 

.067 

.080 .'08 

.136 

.165 

.224 

.287 

7 

.030 

.016 

.062 

.078 

.093 .126 

.159 

.193 

.261 

.333 

8 

.034 

.053 

.071 

.089 

.107 .144 

.181 

.220 

.298 

.382 

9 

.039 

.059 

.079 

.101 

.120 .163 

.205 

.247 

.835 

.427 

10 

.014 

.066 

.089 

.112 

.134 .181 

.227 

.275 

.373 

.475 

12 

.053 

.080 

.106 

.134 

.161 .217 

.273 

.330 

.448 

575 

14 

.061 

.093 

.124 

.156 

.187 .253 

.318 

.387 

.523 

.666 

16 

.069 

.106 

.142 

.178 

.214 .288 

363 

.440 

.596 

.763 

18 

078 

.120 

.159 

.201 

.242 .326 

.409 

.435 

.670 

.850 

20 

.388 

.132 

.177 

.223 

.267 .361 

.454 

549 

.746 

.950 

24 

1 .105 

.159 

.2.3 

.268 

.321 .433 

.545 

.660 

.895 

1.150 

30 

.132 

.198 

.267 

.336 

.402 .543 

.681 

.8'5 

1.120 

1.420 

36 

.156 

.238 

.318 

.402 

i .483 i .651 

.8 9 

.990 

1.340 

1 710 

42 

I .181 

.279 

.372 

.469 

.562 .759 

.955 

1.160 

1.570 

2.090 

48 

j .210 

.317 

.425 

.535 

.641 .8G5 

1 

1.090 

1.330 

1.790 

2.290 












































HYDRA ULIC MINING. 


77 


1 For example : What thickness of iron should 
be used to make a 20-inch pipe which must 
bear 200 feet head of water ? The figure given 
in the table is .17? inch, which, by the follow¬ 
ing table, corresponds to between No. 5 and No. 
6 iron. Or, the head being 100 feet and the 
pipe 10 inches in diameter, the thickness will be 
.044 inches, which corresponds nearly to No. 22. 
In selecting the iron it will always be safer to 
take the size one larger than that called for by 
the figures. 

Table showing the thickness, in decimals of 
an inch, of the different sizes of sheet-iron from 
No. 4 up to No. 30 : 


No. 

4 has a thickness of 

.250 

of an 

inch 

i i 

5 

i 4 

4 4 4 4 

.200 

44 

44 

a 

G 

44 

44 4 4 

.166 

44 

44 

i i 

7 

44 

44 4 4 

.142 

44 

4 4 

44 

8 

44 

4 4 44 

.133 

44 

44 

4 4 

9 

44 

4 4 4 4 

.111 

44 

• 

44 

44 

10 

44 

44 44 

.100 

44 

44 

44 

11 

44 

4 4 4 4 

.090 

44 

44 

44 

12 

44 

44 4 4 

.083 

44 

44 

44 

13 

44 

4 4 4 4 

.076 

44 

( 4 

44 

14 

44 

4 4 44 

.071 

4 4 

4 4 

44 

15 

44 

44 4 4 

.066 

44 

44 

44 

16 

44 

44 44 

.062 

44 

44 







7 » 


HYDRAULIC MINING. 


No. 17 has a 

thickness of 

.058 

of an inch 

44 

18 

< < 

4 4 

.055 

44 

44 

<4 

19 “ 

< 4 

44 

.052 

44 

44 

4 4 

20 

it 

44 

.050 

44 

44 

a 

21 

4 4 

44 

.047 

44 

44 

a 

22 

4 4 

44 

.045 

4 4 

44 

a 

23 

it 

44 

.044 

44 

44 

a 

24 

it 

44 

.041 

4 4 

44 

a 

25 “ 

it 

44 

.040 

44 

44 

it 

26 

it 

44 

.038 

44 

44 

a 

27 

it 

44 

.037 

44 

44 

a 

28 

it 

44 

.035 

44 

44 

n 

29 

it 

44 

.034 

44 

44 

a 

30 

it 

44 

.033 

44 

44 


It must be remembered that these figures ap¬ 
ply only in cases where the end of the pipe is 
closed and no discharge occurs, or where the 
discharge is on the same level as the inflow. Of 
course if the pipe is discharging at one end the 
pressure is relieved, and the pipe is called upon 
to sustain only that bursting pressure due to its 
depression below the hydraulic grade-line. As 
in practice the depression of the pipe leading 
from the water-box to the pit is rarely more than 
5 to 20 feet below the hydraulic grade-line, the 
iron will be compelled to resist a pressure never 
over 10 lbs. to the square inch. This, ordinary 
stove-pipe iron would generally do. 







/ 


CHAPTER VIII. 

NOZZLES AND DISCHARGE. 

Theoretically, the quantity of water dis¬ 
charged from the nozzle of a pipe may be de¬ 
termined by the following rule: 

Rule 1 . Extract the square root of the head, 
and multiply this root by 8.03. The product 
will be the velocity in feet per second with 
which the water escapes from the mouth-piece. 

Multiply the area of the mouth piece (see 
page 41) by this velocity, and the result will be 
the discharge in cubic feet per second. 

Example. —What quantity of water will be 
discharged from a pipe, under a head of 100 
feet, through a 3-inch nozzle ? 

The square-root of the head (100) is 10, 
which, multiplied by 8.03, gives 80.3 feet as 
the velocity per second. The diameter of nozzle 

79 





8o 


HYDRAULIC MINING. 


being 3 inches (.25 of a foot), its area would 
be .25 multiplied by 3.14 multiplied by .0625 = 
.04906 square feet, which, multiplied by the ve¬ 
locity 80.3, equals 3.93 cubic feet, which is the 
discharge per second. 

The actual discharge is probably about 80 per 
cent, of the theoretical one in well-made nozzles, 
provided with inside flanges to prevent revolu¬ 
tion of the stream, and in this case would be 
3.14 cubic feet per second. 

This, reduced to miners’ measure (see page 18), 
would represent about 115 inches. The power 
of the stream thrown by a nozzle has been dis¬ 
cussed under the head of Momentum (page 39), 
and nothing remains to be said on the subject, 
except that every precaution should be taken to 
prevent the stream from issuing in a ragged con¬ 
dition. Its effectiveness depends very largely 
upon its smooth and cylindrical form. If this 
is secured it will travel through the air for 
a much longer distance without disintegration 
than otherwise. The mouth-piece, therefore, 
should be very smooth, and the arrangements 
of the pressure or water box so perfect as to 



HYDRAULIC MINING. 


8l 


exclude all sand and gravel, and, if possible, all 
air. Fine specks of quartz passing through the 
mouth-piece will not only cut the metal, but will 
spoil the shape of the jet. 









CHAPTER IX. 


THE SLUICE. 

Upon the construction and operation of these 
channels almost everything in placer-mining de¬ 
pends. It is a comparatively simple matter to 
disintegrate the most cohesive gravel-bank and 
deliver it at the head-box, but by no means so 
easy to so conduct the washing as to save even a 
respectable amount of gold. In former days 
miners were content with saving from 30 to 50 
per cent., for the ground worked at those times 
was rich enough to pay handsomely even then. 
The miner of to-day, however, has to deal with 
a lower grade of material worth from 35 to 50 
cents to the cubic yard, and must work closer to 

produce a profit. In California ground worth 

. 

only 4 cents to the cubic yard is worked suc¬ 
cessfully. In Colorado and Montana there is no 
need as yet (and in fact there is none in Cali¬ 
fornia) to touch such poor gravel, for there are 

82 






HYDRAULIC MINING. 


83 


millions of acres still unopened which, will pro¬ 
duce 30 to 80 'cents. This circumstance, how¬ 
ever, affords no legitimate excuse for careless 
working. It will be found at the present day 
to be just as expensive to save 50 as 00 per cent, 
in mines where there is any pretence to careful 
work. And the sooner the business of gravel- 
washing is reduced to a science, the sooner it 
will attract the attention of investors and re¬ 
ceive the benefit of their assistance. 

Steadiness of flow in a sluice is of great im¬ 
portance. The quantity of water passing, and 
its velocity, must be uniform to secure the de¬ 
position of a maximum of gold. Again, it is no 
economy to crowd a flume with dirt beyond cer¬ 
tain limits, which will be noted further on. If 
the gravel is caved in too large quantities it will 
be found economical to erect other sluices. It is 
to be remembered, also, that water always tra¬ 
vels faster in the centre of the channel, and is 
also higher in level. Consequently the bulk of 
the gravel and boulders will travel down the 
middle of the flume. 

Dimensions .—The maximum quantity of wa- 


8 4 


HYDRAULIC MINING. 


ter which may bo advantageously used in a sin¬ 
gle sluice of correct dimensions when the ground 
is ordinarily full of boulders, is set down by good 
practical authorities at 1,000 miners’ inches. 
This corresponds to a discharge of 95,000 cubic 
feet per hour, which, with gravel and boulders, 
would represent about double that amount of 
moving substance in the sluice. When more 
than this is used the current will be so strong 
that men cannot work to any advantage in the 
head-box. Sluices intended to clear off top dirt 
must be short and large. In this case the top 
dirt is presumed to be nearly free of gold and 
of boulders. 

The test’of friction is perhaps the correct one 
on which to base calculations for the correct di¬ 
mensions. The general behavior of this force 
is referred to on page 38, and on page 52 will be 
found the law of the least wet perimeter. In a 
sluice, the object being to move all the gravel 
from the head-box to the dump by means of the 
forces of water and gravity, it is important that 
the least amount of the former should be lost in 
overcoming extraneous resistance. We may in- 




HYDRAULIC MINING. 


85 


crease the work of the water by giving it veloci¬ 
ty through the instrumentality of heavy grade, 
but if the flume is of incorrect dimensions tin re 
is always a loss for which the miner receives no 
compensation, and which may be avoided. 

To secure this point let the miner first decide 
upon the largest sized boulder which he will 
allow to go through his flume. If it be 2 feet 
in diameter, then it is clear that his flume must 
carry at least 2 feet in depth of water. We 
have then a figure for a side measurement. Ac¬ 
cording to the law on page 52 the bottom should 
be from If to 2| times the height of the side, or, 
taking the side at 30 inches, the bottom should 
be 52J to 07-|- inches wide. If, however, the 
ground is free from large boulders, and it be 
merely necessary to ascertain the dimensions 
best adapled to cany the greatest economical 
quantity of water (1,000 inches), Rules 2 and 3, 
on pages 41 and 42, will furnish the correct area 
of section. 1,000 inches is equal to 27.1 cubic 
feet per second. Double this discharge to make 
room for the gravel. The flume must then dis¬ 
charge 54.2 cubic feet of material per second. 


86 


HYDRAULIC MINING. 


Having ascertained the area of section in square 
feet, we may resolve it into correct dimensions 
by the following rules : 

Rule 1 . The width to he 2f times the sides. 

Multiply the area in square inches by 4, and 
divide the product by 9. Extract the square 
root of the quotient. The result will be the 
height of side in inches. 

Rule 2. The width to he If times the sides. 

Multiply the area in square inches by 4, and 
divide the product by 7. Extract the square 
root of the quotient. The result will be the 
height of side in inches. 

Those who have a preference for shallow boxes 
will adopt Rule 1, and those who incline towards 
deep ones will take Rule 2. 

Grade .—Grade creates velocity. Velocity in¬ 
creases the work of water, and consequently 
where the quantity of water is small it must be 
assisted by giving it a greater fall. As practi¬ 
cally the whole question of power with water in 
sluices depends upon the velocity with which it 
moves, the question of grade is of great impor¬ 
tance. The miner, however, does not merely 




HYDRAULIC MINING . 


87 


seek for power in his sluice. While there is 
boulder and gravel to wash away there is gold 
to be saved. Consequently, that velocity is the 
best which will wash away a maximum quantity 
of gravel and rock and a minimum of gold. Let 
the miner, therefore, study for a while the com¬ 
position of his banks. 

If the boulders are rounded and well worn 
they will roll down the sluice with ease under a 
small head, but if fl it they will need more power. 
And the same is true if they he angular, though 
not to so great an extent. 

Scale and leaf gold will float a long distance 
in a turbid and rapid stream. 

Generally the physical quality of gold may he 
determined by an examination of the gravel. 
The miner should not trust to that caught in his 
riffles, for much may he washed away which he 
can never examine. If the gravel and boulders 
are angular and large the gold will have the 
same characteristics ; but if the former are pol¬ 
ished the gold is round or leafy, and much will 
be a fine dust. 

The moving power of water in sluiceways may 


88 


HYDRAULIC MINING. 


be approximately judged by the following 
table: 

10 feet per minute begins to wear away fine clay. 


30 

< 6 

u 

just lifts fine sand. 

39 

66 

a 

lifts sand as coarse as linseed. 

45 

a 

a 

moves find gravel. 

120 

< c 

u 

“ inch pebbles. 

200 

< * 


“ pebbles as large as eggs. 

320 

< < 

66 

“ boulders 3 to 4 inches thick. 

400 

<( 

6 6 

“ “ 6 to 8 

600 

6 * 

66 

“ “ 12 to 18 “ 


We have, then, the following rule for the es¬ 
tablishment of grades in sluices when the veloc¬ 
ity needed is decided upon: 

Rule 3.—Multiply the velocity expressed in 
feet per second by itself, and the product by 
the wet perimeter in feet. 

Divide this result by twice the area in square 
feet. The result is the total fall in feet per 
mile. 

Example. —What grade must be given to a 
sluice 12 inches broad and G inches deep, that it 
may carry a velocity of 320 feet per minute, 
or 5.3 feet per second ? 

Multiplying the velocity (5.3). by itself, and 





HYDRA ULIC MINING . 


89 


the product by the wet perimeter (24 inches =2 

l'eei), we have 56.18. This, divided by the area 

% 

(72 square inches =.5 of a foot), and doubled 
= 56.18, which is the fall in feet per mile. 

To reduce grades expressed in feet per mile 
to inches per box of 12 feet, multiply by the 
decimal .027. Thus, a grade of 56.18 feet per 
mile equals a grade of 1.5, or inches per 
box. To reduce to inches per rod (16 feet), 
multiply by the decimal .036. 

Prof. Silliman’s calculations on California 
cement gravel, after being disintegrated by 
blasting, indicate that 1T| cubic yards of wa¬ 
ter, equal to nearly 15 tons, are necessary to 
wash 1 cubic yard of gravel. For ordinary 
gravel, after being caved, probably 8 to 12 
tons would suffice. 

When the course of the sluice is curved the 
outer edge must be raised, to prevent unequal 
wear and an accumulation of material. This 
is much more imperative in the sluice than in 
the flume. 

Riffles .—It is not possible within the limits 
of this work to discuss the subject of riffles 


90 


HYDRAULIC MINING. 


thoroughly. Nor is it yet decided which of 
the systems (wood, boulder, or railroad iron) 
presents the most advantages in thcf majority 
of cases. The first is the most extensively 
used, and will probably always hold its j)lace. 
Some experiments made in California with 
railroad iron demonstrate that that style of 
riffle was strongly to be recommended for very 
rocky ground at least. The great efficacy of 
boulder riffles is well known, and is thorough¬ 
ly illustrated in the ground-sluice. 

As already stated, the bulk of gravel and 
boulders travels down the centre of a sluice, 
where there is at once the most water and 
the greatest velocity. Consequently, it will be 
found advantageous to have the riffles higher 
in the centre than in the sides. This will 
cause a distribution of deposit over the en¬ 
tire width of box, and will also prevent the 
formation of a channel of depression in the 
bottom of the sluice. 

The cost of wooden block-riffles, cut from 
peeled round lumber and squared, will average 
about $50 per 1,000. A thousand of these 





HYDRAULIC MINING. 


91 


blocks will cover 80 square yards of bottom. 
Laying and fastening, and all other expenses 
concurrent with arran^in^ the bottom of the 
sluice for work, will bring the total cost to 75 
cents per square yard. It will be impossible 
to quote the expense of railroad-iron riffles. 
Old rails are, of course, just as good as new. 
The cost will be mainly that of transporta¬ 
tion. 


92 


HYDRAULIC MINING . 


TABLE I. 


TABLE OF SQUARE ROOTS. 


The following table of the square roots of numbers from 1 to 200, in¬ 
clusive, will probably answer all requirements of problems proposed 
in the preceding examples. If the iigure whose root is to be extracted 
is not found in the table, take the root of the iigure nearest to it. 
For example, if it is necessary to extract the root of 132.6, take the 
root of 133. 


No. 

Root. 

No. 

Root. 

No. 

Root. 

No. 

Root. 

No. 

Root. 

1 

1 . 

1 41 

6.4031 

1 81 

9. 

1 121 

11. 

1 161 

12.6886 

2 

1.4142 

42 

6.4807 

82 

9.C554 

122 

11.0454 ( 

! 162 

12.7.79 

3 

1.7321 

( 43 

6.5574 

83 

9.1104 

123 

11.6905 ! 

163 

12.7671 

4 

2. 

' 44 

6.6332 

84 

9.1652 

124 

11.1355 

164 

12.8062 

5 

2.2361 

45 

6.7082 

85 

9.2195 

125 

11.1803 

165 

12.8452 

6 

2.4195 

46 

6.7823 

86 

9. .736 

126 

11.2250 

166 

12.8811 

7 

>.6458 

47 

6.8557 

87 

9.3274 

127 

11.2o94 1 

167 

12.9228 

8 

2.8284 

48 

6.9282 

88 

9.3808 

128 

11.3.3? 

168 

12.9615 

9 

3. 

49 

7. 

89 

9.4340 

129 

11.8578 

169 

13. 

10 

3.1623 

50 

7 0711 

90 

9.4868 

130 

11.4018 

170 

13 0384 

11 

3.3166 

51 

7.1414 

91 

9.5394 

131 

11 4455 

171 

13.0767 

12 

3 4611 

52 

7.2111 

92 

9.5917 

132 

11.4891 

172 

13.1149 

13 

3.6056 

53 

7.2801 

93 

9.6437 

133 

11.5326 

171 

13.1529 

14 

8.7417 

54 

7.3485 

94 

9.1 954 

134 

11.5758 

174 

13 1909 

15 

3.8730 

55 

7.4162 

95 

9.7468 

135 

11.6190 

175 

13.2288 

16 

4. 

56 

7.4833 

93 

9.7980 

136 

11.6619 

176 

13.2665 

17 

4.1231 

57 

7.5498 

97 

9.8489 

13? 

11.7047 

l?7 

13.3041 

18 

4.2426 

58 

7.6153 

98 

9.8995 | 

138 

11.7473 

178 

13.3417 

19 

4.3589 

59 

7.68.1 

99 

9 9499 

139 

11.7898 

179 

13 3791 

20 

4.4721 

60 

7.7400 

100 

10. 

140 

11.8322 

180 

13.4164 

21 

4.5826 

61 

7.8102 

10L 

10.0499 

141 

11.8743 

181 

13.4536 

22 

4 6904 

62 

7.8710 

02 

10.0995 

142 

11.9164 

'82 

13.49 ? 

23 

4.7958 

63 

7.9373 

103 

10.1489 

143 

11.9583 

183 

13.527? 

24 

4.8990 

64 

8. 

104 

101980 

144 

12. 

184 

13.5647 

I 25 

5. 

65 

8.0623 

1(»5 

10.2471) 

145 

12.0416 

185 

13.6015 

26 

5 0990 

66 

8.1240 

106 

10.2956 

146 

12.0830 1 

186 

13.6382 

27 

5.1862 

67 

8.1854 

10? 

10.3441 

147 

12.1244 

18? 

13.6748 

28 

5.2915 

68 

8.2462 

108 

10.3923 

148 

12.1655 1 

188 

13.7113 

29 

5.3852 

69 

8.3066 

109 

10 4403 

149 

12.2066 

1 9 

13.747? 

30 

5.4772 

70 

8.3666 

110 

10 4881 

150 

12.2474 

190 

13.7840 

31 

5.5678 

71 

8.4261 

111 

10.5357 

151 

12.2882 

191 

13.8203 

: 32 

5.6569 

72 

8.4853 

112 

10.58:10 

152 

12.3.-88 

192 

13.8564 

33 

5.7446 

73 

8.5440 

113 

10.6301 

153 

12.3-93 

193 

13.8924 

34 

5.8310 

74 

8.6023 

114 

10.6771 

154 

12 4097 

194 

13.9284 

05 

5.9161 

75 

8.6603 

115 

10.7238 

155 

12.4499 

195 

13.9642 

i 06 

6. 

76 

8 7178 

116 

10.7703 

156 

12.4900 

196 

14. 

; & 

6.0828 

77 

8.7750 

117 

10 8167 

15? 

12 5300 

197 

14.0357 

38 

6.1644 

78 

8.8318 

118 

10.8628 

158 

12.5698 

198 

14.0712 

! 39 

6.2450 

79 

8 8882 

119 

10.9087 

159 

12 6095 

199 

14.1067 

j 40 

6 324G 

80 

8.9443 

120 

10.9545 

160 

12.6491 

! 200 

14.1421 

















































HYDRA ULIC MINING. 


93 


TABLE II. 

PIFTn ROOTS. 

The following table of numbers and roots will cover all problems 
that come to the miner. The numbers are printed in heavy type and 
the roots in light. If the exact number is not found, take the roots of 
the number nearest to it: 


No. 

Root. 

No. 

Root. 

No. 

Root. 

7.59 

1.5 

5032.84 

5.5 

69049. 

9. 

32. 

2. 

7776. 

6. 

77378. 

9.5 

97.65 

2.5 

11603. 

6.5 

100000. 

10. 

243. 

3. 

16807. 

7. 

13663S. 

10.5 

525.21 

3.5 

23730. 

7.5 

161051. 

11. 

1024. 

4. 

32768. 

8. 

201035. 

11.5 

1845.28 

4.5 

44370. 

8.5 

248832. 

12. 

3125. 

5. 






























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